Such a luminaire is known from KR2009083546. The known luminaire has a high-brightness LED illumination module as the light source to obtain uniform luminance of the plurality of reflecting lamellae. The lamellae holding means is embodied as a concave reflector for gathering the light and is installed in the longitudinal direction as an inner side of a housing. The lamellae are provided in a row in an inclined orientation alongside a longitudinal direction of the luminaire inside a space enclosed by the housing. Especially for luminaries having high brightness light sources, said uniform luminance is difficult to obtain. In the known luminaire said uniform luminance is obtained by an increased size of each lamella more remote from the light source, thus enabling each lamella to intercept part of the light of the diverging light beam that has passed lamellae closer to the light source. A first part of the light emitted by the light source impinges on the reflective surface of the adjacent lamella and is reflected to the exterior through the light emission window. A second part of the light emitted by the light source propagates alongside said adjacent lamella and partially impinges on the next lamella and partially propagates to yet another lamella. It is a disadvantage of the known luminaire that the lamellae are mutually different, as their dimensions increase with increasing distance from the light source lamellae. This has the disadvantage that the luminaire is relatively expensive because relatively much material is required for its construction and because the lamellae have no (same) standard size. It is another disadvantage of the known luminaire that it is relatively bulky, resulting in the additional disadvantage that the known luminaire is relatively difficult to build into false ceilings where only relatively little space is available.